For linear elastic materials, only two properties are required to describe the stress-
strain behavior under any loading condition. The Young's modulus is typically used to
describe changes due to the normal stresses and the shear modulus (G) describes the
change in the material due to shear stresses. Similarly, the inclusion of Poisson effects is
captured by the Poisson's ratio (u). In viscoelastic materials, G* and E* are the most
commonly used parameters. The magnitude of G* is calculated using the shear stress
amplitude (To) and the shear strain amplitude (Yo) in Equation 2-4 by Witczak et al.
(1999).
G = 0 (Eq. 2.4)
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Similar to the complex modulus, G* has an elastic component (G') and a viscous
component (G") by Witczak et al. (1999). These components are related through the
phase angle (6) as seen in Equation 2-5.
3 = tan \G'1 (Eq. 2-5a)
\G'j
G"= G sin(3) (Eq. 2-5b)
G'= G *cos(3) (Eq. 2-5c)
To calculate both the E* and the G* coefficients, it must be possible to measure not
only the axial compressive stresses and strains, but also the shear stresses and strains.
Harvey et al. (2001) concluded that G* can be related to E* using Equation 2-6.
G* = 2(1 (Eq. 2-6)
By directly measuring changes in the height and radius of the asphalt sample,
Poisson's ratio can be calculated. This is done by calculating v as the ratio of lateral